Deciphering the maximal transcendentality principle via bootstrap. (English) Zbl 1531.81226
Summary: We prove the principle of maximal transcendentality for a class of form factors, including the general two-loop minimal form factors, the two-loop three-point form factor of \(\operatorname{tr}(F^2)\), and the two-loop four-point form factor of \(\operatorname{tr}(F^3)\). Our proof is based on a recently developed bootstrap method using the representation of master integral expansions, together with some unitarity cuts that are universal in general gauge theories. The maximally transcendental parts of the two-loop four-gluon form factor of \(\operatorname{tr}(F^3)\) are obtained for the first time in both planar \(\mathcal{N} = 4\) SYM and pure YM theories. This form factor can be understood as the Higgs-plus-four-gluon amplitudes involving a dimension-seven operator in the Higgs effective theory. In this case, we find that the maximally transcendental part of the \(\mathcal{N} = 4\) SYM result is different from that of pure YM, and the discrepancy is due to the gluino-loop contributions in \(\mathcal{N} = 4\) SYM. In contrast, the scalar-loop contributions have no maximally transcendental parts. Thus, the maximal transcendentality principle still holds for the form factor results in \(\mathcal{N} = 4\) SYM and QCD, after a proper identification of the fundamental quarks and adjoint gluinos as \(n_f\rightarrow4N_c\). This seems to be the first example of the maximally transcendental principle that involves fermion-loop contributions. As another intriguing observation, we find that the four-point form factor of the half-BPS \(\operatorname{tr}(\phi^3)\) operator is precisely a building block in the form factor of \(\operatorname{tr}(F^3)\).
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81T18 | Feynman diagrams |
| 81U05 | \(2\)-body potential quantum scattering theory |
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